Pascal's law: Definition,experiment,hydraulic machine and examples.
Pascal's law
Pascal's law
EXPERIMENT
Demonstration of Pascal's law
Need:
1.A glass flask, provided with tubes arising from sides and bottom.
2.A air-tight piston at its mouth.
Work to be done:
1.Fill the flask with water till the black-dotted line in the diagram.
2.Finally push the piston gently.
Observation:
The jet of water rises to a same height as shone in the diagram by the colored-dotted line.
PRINCIPLE OF A HYDRAULIC MACHINE
The principle of each hydraulic machine is that a small force applied on a smaller piston is transmitted to produce a large force on the bigger piston.Mathematically
In the diagram, shows tho cylindrical containers P and Q connected by a tube R.The containers contain a liquid(water) and the containers are provided with air-tight pistons A and B.
Principle of Hydraulic machine
Let the area of the smaller diameter-piston P be A1 and that of the bigger container Q is A2
. When a weight is placed on the piston A it provides a force of F1 on it.Thus pressure applied on the piston is
P1 =F1 / A1 ...(i)
According to Pascal's law ,pressure exerted on piston A is transmitted through the liquid to the piston B.This exerts an upward pressure P2 on the piston B which is equal to P1 . Thus,
P1 = P2
...(ii)
If the upward force exerted on the piston B is F2 ,Then,
F2 = P2* A2
...(iii)
...(iii)
From equations (i),(ii) and (iii) F1 /A1= F2 / A2
or F2 / F1 = A2 / A1 ...(iv)
Since A2 >A1,therefore F2 >F1
Thus a small force F1 applied on the smaller piston A can be used to produce a large force F2 on the bigger piston B.This is the principle of hydraulic machine which acts as a force multiplier.
EXAMPLES
(i)Hydraulic press
Hydraulic press
Construction:
In the diagram we can see two hollow cylinders P and Q provided with valves V1 and V2 at the bottom.A reservoir has bee provided below the cylinder P.The area of cross section of the cylinder P is smaller than the cylinder Q. The cylinders are fitted with water tight pistons A and B.Let the area of cross section of the pistons A and B be A1 and A2 ,respectively.The cylinders are connected with the pipe R.The piston A of the smaller cylinder is called the pump plunger and piston B of the larger cylinder is called the ram (or press plunger). For pressing the down or rise up the pump of the piston A, a arrangement of a lever is used provided with handles.A release valve is contained at the bottom of the cylinder Q which is joined with the reservoir.
Basic principle:
When a force of F1 is applied on the piston A, it provides a pressure on the liquid containing in the cylinder P.Following the Pascal's law the pressure is transmitted to the piston B,due to which the piston looks to move upward.As the area of cross section of the cylinder P is less than that of cylinder Q,a small force applied on the piston A can provide a large upward force on the other piston B.
When no weight is placed on the piston B,it rises up against a fixed roof with a force F2 ( F2 >F1 ).If a bale of cotton is kept on the press plunger B,it gets compressed.
Working:
ON rising the piston A by rising the handle H,the pressure decreases and the valve V1 opens upward.Now the water from the reservoir rises upward in to the cylinder P due to atmospheric pressure acting on the surface of the water in the tank.When the piston A is pushed downward by pressing the handle H, the valve V1 closes due to an increase in pressure in the cylinder P.Now pressure from cylinder P is transferred to the connecting pipe R.As the pressure in the pipe R becomes greater then in cylinder Q,the valve V2 opens,so water from cylinder P is forced into the cylinder Q,due to which the press plunger B is raised against the bale of cotton placed on the press plunger B gets compressed.
(ii)Hydraulic Jack
Hydraulic jack
Hydraulic jack is used to lift up heavy vehicles like cars,trucks,etc.in service station for the repairing.
Construction:
In the diagram we can see there are two cylinders P and Q,connected by a tube R provided by a valve V.The piston A of the narrower cylinder consists of a lever provided with a handle H,on the other hand the wider piston consists a platform for vehicles.the cylinders contains water(or any liquid).
Working:
When the handle H of the piston A is pressed the valve V opens and the the pressure applied is transmitted to the other piston B through water according to the Pascal's law.The water from the cylinder P runs to the cylinder Q. As a result the piston B rises to a height.After rising to the desired height the handle H is no longer pressed.The valve gets closed so that the liquid don't get released from the cylinder Q to cylinder P.
(iii)Hydraulic brakes
Hydraulic brake
Construction:
In the diagram we can see that the hydraulic brakes consist of a pipe line R containing a liquid (say oil) one end of which is connected to the master cylinder P fitted with a piston A attached to the foot pedal.On the other end the pipe R is connected to the brake arrangement.The diagram shows only one wheel's brake arrangement.There is a wheel cylinder Q having two piston B1 and B2 attached to the brake shoes.
Working:
When the foot pedal is pressed due to which the pressure is exerted in the master cylinder P.The pressure is the transmitted to the wheel cylinder through the pipe R.As a result the pressure is transferred to the pistons B1 and B2 .Following which the pistons are pushed outward and brake shoes get pushed against the rim of the wheels due to which the motion of the vehicles get retard.As the area of cross section of the master cylinder P is smaller the small force applied can be transferred to a large force on the pistons.
On releasing the pressure on the pedal,the spring pulls the brake shoes to their original position and forces the pistons B1 and B2 to return back into the wheel cylinder Q. As a result the liquid runs back from the wheel cylinder Q to the master cylinder P and thus the brakes get released.
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